Question

When 229 J of energy is supplied as heat at constant pressure to 3 mol Ar(g), the temperature of the sample is increased by 2.55K. Calculate the motor heat capacity at constant volume :

• A. 30 KJ K${}^{-1}$ mol${}^{-1}$
• B. 30 J K${}^{-1}$ mol${}^{-1}$
• C. 21.7 J K${}^{-1}$ mol${}^{-1}$
• D. 21.7 KJ K${}^{-1}$ mol${}^{-1}$

Answer 1

The correct option is B 30 J K${}^{-1}$ mol${}^{-1}$

Solution:- (B) $30J/mol-K$

Given:-

Heat supplied $\left(q\right)=229J$

No. of moles $\left(n\right)=3\text{mol}$

$dT=$ Small change in volume $=2.55K$

$C_V=$ Molar heat capacity at constant volume $=?$

As we know that, at constant volume,

$q=n{C}_{V}dT$

$\therefore C_V=\frac{q}{ndT}$

$\Rightarrow C_V=\frac{229}{3\times 2.55}=30J/mol-K$

Hence the molar heat capacity at constant volume is $30J/mol-K$.